Time-of-flight mass spectrometers acquire individual time-of-flight spectra in rapid succession. To avoid saturation effects for the most intense ion signals, the spectra must each only contain a maximum of a few hundred ions, and therefore they have a large number of empty gaps and a strong variance. For ion signals of low intensity an ion is measured only in one in ten, one in a hundred or even one in a thousand single time-of-flight spectra. Thousands of these individual time-of-flight spectra, which are acquired with very high scanning rates of up to ten thousand spectra per second and more, are then immediately processed into a sum spectrum in order to obtain useful time-of-flight spectra with signals which are true to concentration across a large measurement range for the ion species of the different substances under analysis.
The term “ion signal” is used here to mean that part of an ion current curve which contains ions of one charge-related mass m/z. This ion signal is also called “ion peak”.
To measure the time-of-flight spectra, the ion currents are first amplified by secondary electron multipliers (SEM) by a factor of between 105 and 107, and then sampled by special digitization units, which are called “transient recorders”. These incorporate very fast analog-to-digital converters (ADC) which today operate with sampling rates of around 4 gigasamples per second (GS/s); higher sampling rates of up to around 10 gigasamples per second are currently under development. The digitization depth per measurement is usually only eight bit, i.e. it spans only values from 0 to 255; a good dynamic range of measurement of five to six orders of magnitude can therefore be achieved only by the summation of hundreds or thousands of individual spectra.
On the one hand, a limited ion current is required so as not to saturate the analog-to-digital converter in the individual time-of-flight spectra. But, on the other hand, every individual analyte ion is required to be measured reliably. In order not to lose any ions nor reach saturation during the measurement, the amplification of the SEM must be set very accurately. Methods for optimally setting the amplification of the SEMs are known (see A. Holle, DE 10 2008 010 118 A1; GB 2 457 559 A; US 2009/0206247 A1, for example). The Poisson distribution of the secondary electrons formed by an impacting ion means it is advantageous if an individual ion produces a signal which generates a measured value of at least 2 to 3 counts in the ADC. However, this limits the intensity dynamics in an individual time-of-flight spectrum to two orders of magnitude: from around 2.5 counts to 255 counts. Since there exists an electrical noise of up to three counts, the dynamic measuring range is even smaller: only one and a half orders of magnitude.
This optimum setting of the secondary electron multiplier only applies to ions of a selected charge-related mass m/z, however, because the sensitivity of the SEM is dependent on mass and decreases roughly with 1/√(m/z). If, for example, the amplification of an SEM is set so that the above-mentioned 2 to 3 counts are achieved for an ion of the charge-related mass m/z=5,000 daltons in order not to lose any ions of high mass, in particular, this means that an ion of mass m/z=50 daltons already results in around 25 counts, and the measurement range for ions of this mass is limited to only one order of magnitude from 25 to 255 counts. Taking the electric noise into account, there remains a dynamic range of only half an order of magnitude.
Until a few years ago this limitation was not such a problem, because the best ion sources supplied only limited quantities of ions per unit of time, and the transmission of the best mass spectrometers was still so low that saturation of the ADC could hardly be reached. This applied both to ion sources with ionization by electrospray ionization (ESI) and also to ionization by matrix-assisted laser desorption (MALDI). Saturation is, in fact, only achieved if there are a few hundred ions in an ion signal of one mass because, as is explained below, this signal is distributed over some eight measurement periods at least, where each has 0.25 nanoseconds duration. However, 800 singly-charged ions per nanosecond correspond to an ion current of around 5 nanoamperes, quite a high ion current for the mass spectrometry of macromolecular substances. The ongoing development of ion sources and also mass spectrometers, however, means the saturation limit is being reached and exceeded more and more often; one therefore has to look for methods which make it possible to approach the saturation limit or even exceed it several times over.
In mass spectrometers of this type, secondary electron multipliers (SEM) are used without exception to measure the ion currents. These can be constructed in various ways; the specialist is familiar with these detectors, however, so that it is not necessary to explain them in more detail here. The process of avalanche-type secondary electron multiplication results in amplification, but also broadening, of the electron current signal. From a single impacting ion, the best secondary electron multipliers generate a signal of around 0.5 nanoseconds full-width at half maximum; the signal width of less expensive secondary electron multipliers is around 1 to 2 nanoseconds. It is not to be expected that significant progress will be made here in the future because the technology is essentially fully developed.
If one samples the electron current curve from the SEMs point by point, by means of a transient recorder with 8 gigasamples per second, for example, one obtains minimum signal widths at half height of 0.5 nanoseconds for each individual ion, regardless of the mass of the ion, if one uses the best devices. If the signal profiles of individual ions are summed in successive individual time-of-flight spectra, or if there are several ions of the same mass in an individual time-of-flight spectrum, the signal widths are even larger. This is because focusing errors of the mass spectrometers, not fully compensated effects of initial energy distributions of the ions before their acceleration into the flight path, and other influences also play a part. These effects result in additional signal broadenings in the order of at least one nanosecond, usually dependent on the mass of the ions. Since in our experience all these contributions add to the signal width in a Pythagorean way (i.e. they form the root of the added squares of the widths), only signal widths of around one nanosecond, at the minimum, can be achieved with the very best spectrometers and detectors; in reality, the signal widths are usually in the range of 2 to 3 nanoseconds. Their full-width at half maximum is almost constant in the lower mass range, where the avalanche width of the SEM dominates; in the upper mass range, on the other hand, it is roughly proportional to the square root of the charge-related mass m/z.
These unavoidable signal widths of the ion signals limit the resolution of the time-of-flight mass spectrometers. The generation of longer times of flight by means of lower accelerating voltages offers a remedy, but has other disadvantages. It is better to use longer flight paths by means of longer flight tubes, although this solution is not very elegant, either. The use of multiply bent flight paths with several reflectors to generate extremely good resolutions has not proven to be a good solution. However, a tried and tested method is an artificial increase of the time of flight resolution and mass resolution by computational means.
Such a computational improvement of the mass resolution can take the following form: a signal analysis is carried out for each individual time-of-flight spectrum. If an ion signal is found, a value which is proportional in terms of area or height is added only where the time of flight of the signal maximum is located. In the simplest case only the measured value of the signal maximum is added at the relevant position of the signal maximum in the individual time-of-flight spectrum. Since the times of flight of the signal maximum are subject to statistical variations, a somewhat broader sum signal results for this ion signal. The sum signal has a finite width but is narrower than when all the measured values were summed. This sum signal only contains the statistical variances, and no longer contains the avalanche width or the width of the imaging errors (see O. Raether: DE 102 06 173 B4; GB 2 390 936 B; U.S. Pat. No. 6,870,156 B2). These conditional additions are not easy to carry out, however, because the complete algorithm must run at four or even eight gigahertz, which is very difficult even when using very fast FPGA (field programmable gate arrays) or very fast digital signal processors (DSP).
It is remarkable that this method not only increases the mass resolution, but also the mass accuracy. Adding together thousands of individual time-of-flight spectra produces a sum time-of-flight spectrum, which is simply called “time-of-flight spectrum” below. Mass spectra are computed from these time-of-flight spectra. The purpose of these time-of-flight mass spectrometers is to determine the masses of the individual ionic species as accurately as possible. The computational measure just described, which was actually introduced to increase the mass resolution, enables mass accuracies of 0.5 ppm or better to be achieved in suitably designed mass spectrometers nowadays.
The term “ppm” (parts per million) for the accuracy is used to mean the relative accuracy of the mass determination in millionths of the charge-related mass m/z. The accuracy is, in turn, set statistically as sigma, the width parameter of the measurement variance, with the implicit assumption of a normal distribution. This width parameter gives the distance between the point of inflection and the maximum of the Gaussian normal distribution curve. The following then applies by definition: if the mass determination is repeated many times, 68% of the values are within the single sigma interval on both sides (i.e. between the points of inflection), 95.57% in twice the sigma interval, 99.74% in three times the sigma interval and 99.9936% in four times the sigma interval of the normally distributed error spread curve. Unfortunately, this method of increasing the mass resolution and the mass accuracy does not increase the dynamic measurement range. One still has to take care not to drive the ion signals into saturation.